''I asked Stretch if he knew anything about being lieutenant governor and he said 'I can cut ribbons and attend funerals.' I said, 'Son, you're my man.' ''

Mann was joking, of course. Like most of the candidates for governor, he has not yet named a running mate. But his line, which drew a big laugh from the crowd, is an apt description of the re- sponsibilities of the lieutenant governor.

The office warrants two sentences in the state Constitution. It simply says the state shall have a lieutenant governor and he will do whatever the governor tells him to do. In another section, it says the lieutenant governor will fill the top job if something happens to the governor.

Given the disharmony between recent governors and lieutenant governors, it is hardly surprising that many candidates for governor this year are having difficulty finding the ideal person to take the job.

Orlando Mayor Bill Frederick has been pursued by two of the Democratic front-runners, Steve Pajcic of Jacksonville and Senate President Harry Johnston of West Palm Beach. Orange County Sheriff Lawson Lamar was considered a top contender for the second spot on Pajcic's ticket until Pajcic's aides got word that the sheriff wouldn't be interested.

Other popular elected officials, businessmen and celebrities have told candidates for governor they do not want the job.

''Gubernatorial candidates have had to offer the position to numerous people in order to find someone who will say yes,'' said Wayne Bailey, a political science professor at Stetson University.

From 1885 to 1968 Florida didn't have a lieutenant governor. The position was put in the 1968 state Constitution because of a general dissatisfaction with the way Senate President Charley Johns handled the job when Gov. Dan McCarty died in office in 1953. For starters, Johns fired most of McCarty's top staffers.

It was thought that if the candidate for governor picked his running mate and the two were elected together, it would ensure a smooth transition if something happened to the governor.

''I'm not so sure it hasn't caused more problems that it's cured,'' said veteran House Clerk Allen Morris. ''It has not been a success in any way.''

The most celebrated running-mate fiasco so far in the 1986 governor's race involves Johnston and Attorney General Jim Smith, who teamed up a year ago in what was widely called a ''dream ticket.'' The ticket had instant credibility because Smith has held statewide office since 1978 and has a strong fund-raising network.

Conflicts over how to run the campaign developed quickly, and the team split before the year ended. Now Smith also is a candidate for governor.

''Jim was too strong in that he wanted to be governor,'' said Steve Uhlfelder, a Tallahassee lawyer and supporter of the Johnston campaign. ''If they're that good, they're going to want to be governor themselves.''

Johnston's second choice for a running mate is entirely different. He picked first-term Rep. Mark Gibbons, D-Tampa, who is just three years older than the 30 years candidates for the office must attain. What Gibbons lacks in age and experience, he may make up for in political capital. He is the son of popular U.S. Rep. Sam Gibbons, D-Tampa, who has served in Congress since 1962. Political credentials traditionally are the most important element a lieutenant governor candidate brings to a campaign. It is generally agreed that Reubin Askew would not have been elected without the political machine of former Secretary of State Tom Adams. The same is considered true of Gov. Bob Graham, a liberal senator from Miami who won conservative votes with the help of Rep. Wayne Mixson of Marianna.

All the candidates for governor this year who have selected running mates have sought to balance the ticket, either geographically or philosophically.

Tampa Mayor Bob Martinez, who was a Democrat until 1983, picked conservative Rep. Bobby Brantley, R-Longwood. Martinez's campaign manager, Mac Stipanovich, acknowledges that a key reason for selecting Brantley is that ''his Republican credentials are impeccable.'' Brantley is a warm, affable person on the campaign trail, while Martinez can be perceived as cool and distant.

Democratic candidate Barry Kutun, a former House member from Miami Beach, picked former Rep. Bobby Hattaway, D-Altamonte Springs, who is in the nursery and real estate business. Kutun, whose primary political base is among liberal Jewish voters in South Florida, clearly hopes Hattaway can bring more conservative Democrats and their money to his campaign.